1 | /*
|
---|
2 | glh - is a platform-indepenedent C++ OpenGL helper library
|
---|
3 |
|
---|
4 |
|
---|
5 | Copyright (c) 2000 Cass Everitt
|
---|
6 | Copyright (c) 2000 NVIDIA Corporation
|
---|
7 | All rights reserved.
|
---|
8 |
|
---|
9 | Redistribution and use in source and binary forms, with or
|
---|
10 | without modification, are permitted provided that the following
|
---|
11 | conditions are met:
|
---|
12 |
|
---|
13 | * Redistributions of source code must retain the above
|
---|
14 | copyright notice, this list of conditions and the following
|
---|
15 | disclaimer.
|
---|
16 |
|
---|
17 | * Redistributions in binary form must reproduce the above
|
---|
18 | copyright notice, this list of conditions and the following
|
---|
19 | disclaimer in the documentation and/or other materials
|
---|
20 | provided with the distribution.
|
---|
21 |
|
---|
22 | * The names of contributors to this software may not be used
|
---|
23 | to endorse or promote products derived from this software
|
---|
24 | without specific prior written permission.
|
---|
25 |
|
---|
26 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
---|
27 | ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
---|
28 | LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
---|
29 | FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
---|
30 | REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
---|
31 | INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
---|
32 | BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
---|
33 | LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
---|
34 | CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
---|
35 | LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
---|
36 | ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
---|
37 | POSSIBILITY OF SUCH DAMAGE.
|
---|
38 |
|
---|
39 |
|
---|
40 | Cass Everitt - cass@r3.nu
|
---|
41 | */
|
---|
42 |
|
---|
43 | /*
|
---|
44 | glh_linear.h
|
---|
45 | */
|
---|
46 |
|
---|
47 | // Author: Cass W. Everitt
|
---|
48 |
|
---|
49 | #ifndef GLH_LINEAR_H
|
---|
50 | #define GLH_LINEAR_H
|
---|
51 |
|
---|
52 | #include <memory.h>
|
---|
53 | #include <math.h>
|
---|
54 | #include <assert.h>
|
---|
55 |
|
---|
56 | // only supports float for now...
|
---|
57 | #define GLH_REAL_IS_FLOAT
|
---|
58 |
|
---|
59 | #ifdef GLH_REAL_IS_FLOAT
|
---|
60 | # define GLH_REAL float
|
---|
61 | # define GLH_REAL_NAMESPACE ns_float
|
---|
62 | #endif
|
---|
63 |
|
---|
64 | #ifdef _WIN32
|
---|
65 | # define TEMPLATE_FUNCTION
|
---|
66 | #else
|
---|
67 | # define TEMPLATE_FUNCTION <>
|
---|
68 | #endif
|
---|
69 |
|
---|
70 | #define GLH_QUATERNION_NORMALIZATION_THRESHOLD 64
|
---|
71 |
|
---|
72 | #define GLH_RAD_TO_DEG GLH_REAL(57.2957795130823208767981548141052)
|
---|
73 | #define GLH_DEG_TO_RAD GLH_REAL(0.0174532925199432957692369076848861)
|
---|
74 | #define GLH_ZERO GLH_REAL(0.0)
|
---|
75 | #define GLH_ONE GLH_REAL(1.0)
|
---|
76 | #define GLH_TWO GLH_REAL(2.0)
|
---|
77 | #define GLH_EPSILON GLH_REAL(10e-6)
|
---|
78 | #define GLH_PI GLH_REAL(3.1415926535897932384626433832795)
|
---|
79 |
|
---|
80 | #define equivalent(a,b) (((a < b + GLH_EPSILON) && (a > b - GLH_EPSILON)) ? true : false)
|
---|
81 |
|
---|
82 | namespace glh
|
---|
83 | {
|
---|
84 |
|
---|
85 | inline GLH_REAL to_degrees(GLH_REAL radians) { return radians*GLH_RAD_TO_DEG; }
|
---|
86 | inline GLH_REAL to_radians(GLH_REAL degrees) { return degrees*GLH_DEG_TO_RAD; }
|
---|
87 |
|
---|
88 |
|
---|
89 | template <int N, class T>
|
---|
90 | class vec
|
---|
91 | {
|
---|
92 | public:
|
---|
93 | int size() const { return N; }
|
---|
94 |
|
---|
95 | vec(const T & t = T())
|
---|
96 | { for(int i = 0; i < N; i++) v[i] = t; }
|
---|
97 | vec(const T * tp)
|
---|
98 | { for(int i = 0; i < N; i++) v[i] = tp[i]; }
|
---|
99 |
|
---|
100 | const T * get_value() const
|
---|
101 | { return v; }
|
---|
102 |
|
---|
103 |
|
---|
104 | T dot( const vec<N,T> & rhs ) const
|
---|
105 | {
|
---|
106 | T r = 0;
|
---|
107 | for(int i = 0; i < N; i++) r += v[i]*rhs.v[i];
|
---|
108 | return r;
|
---|
109 | }
|
---|
110 |
|
---|
111 | T length() const
|
---|
112 | {
|
---|
113 | T r = 0;
|
---|
114 | for(int i = 0; i < N; i++) r += v[i]*v[i];
|
---|
115 | return T(sqrt(r));
|
---|
116 | }
|
---|
117 |
|
---|
118 | T square_norm() const
|
---|
119 | {
|
---|
120 | T r = 0;
|
---|
121 | for(int i = 0; i < N; i++) r += v[i]*v[i];
|
---|
122 | return r;
|
---|
123 | }
|
---|
124 |
|
---|
125 | void negate()
|
---|
126 | { for(int i = 0; i < N; i++) v[i] = -v[i]; }
|
---|
127 |
|
---|
128 |
|
---|
129 | T normalize()
|
---|
130 | {
|
---|
131 | T sum(0);
|
---|
132 | for(int i = 0; i < N; i++)
|
---|
133 | sum += v[i]*v[i];
|
---|
134 | sum = T(sqrt(sum));
|
---|
135 | if (sum > GLH_EPSILON)
|
---|
136 | for(int i = 0; i < N; i++)
|
---|
137 | v[i] /= sum;
|
---|
138 | return sum;
|
---|
139 | }
|
---|
140 |
|
---|
141 |
|
---|
142 | vec<N,T> & set_value( const T * rhs )
|
---|
143 | { for(int i = 0; i < N; i++) v[i] = rhs[i]; return *this; }
|
---|
144 |
|
---|
145 | T & operator [] ( int i )
|
---|
146 | { return v[i]; }
|
---|
147 |
|
---|
148 | const T & operator [] ( int i ) const
|
---|
149 | { return v[i]; }
|
---|
150 |
|
---|
151 | vec<N,T> & operator *= ( T d )
|
---|
152 | { for(int i = 0; i < N; i++) v[i] *= d; return *this;}
|
---|
153 |
|
---|
154 | vec<N,T> & operator *= ( const vec<N,T> & u )
|
---|
155 | { for(int i = 0; i < N; i++) v[i] *= u[i]; return *this;}
|
---|
156 |
|
---|
157 | vec<N,T> & operator /= ( T d )
|
---|
158 | { if(d == 0) return *this; for(int i = 0; i < N; i++) v[i] /= d; return *this;}
|
---|
159 |
|
---|
160 | vec<N,T> & operator += ( const vec<N,T> & u )
|
---|
161 | { for(int i = 0; i < N; i++) v[i] += u.v[i]; return *this;}
|
---|
162 |
|
---|
163 | vec<N,T> & operator -= ( const vec<N,T> & u )
|
---|
164 | { for(int i = 0; i < N; i++) v[i] -= u.v[i]; return *this;}
|
---|
165 |
|
---|
166 |
|
---|
167 | vec<N,T> operator - () const
|
---|
168 | { vec<N,T> rv = v; rv.negate(); return rv; }
|
---|
169 |
|
---|
170 | vec<N,T> operator + ( const vec<N,T> &v) const
|
---|
171 | { vec<N,T> rt(*this); return rt += v; }
|
---|
172 |
|
---|
173 | vec<N,T> operator - ( const vec<N,T> &v) const
|
---|
174 | { vec<N,T> rt(*this); return rt -= v; }
|
---|
175 |
|
---|
176 | vec<N,T> operator * ( T d) const
|
---|
177 | { vec<N,T> rt(*this); return rt *= d; }
|
---|
178 |
|
---|
179 | friend bool operator == TEMPLATE_FUNCTION ( const vec<N,T> &v1, const vec<N,T> &v2 );
|
---|
180 | friend bool operator != TEMPLATE_FUNCTION ( const vec<N,T> &v1, const vec<N,T> &v2 );
|
---|
181 |
|
---|
182 |
|
---|
183 | //protected:
|
---|
184 | T v[N];
|
---|
185 | };
|
---|
186 |
|
---|
187 |
|
---|
188 |
|
---|
189 | // vector friend operators
|
---|
190 |
|
---|
191 | template <int N, class T> inline
|
---|
192 | vec<N,T> operator * ( const vec<N,T> & b, T d )
|
---|
193 | {
|
---|
194 | vec<N,T> rt(b);
|
---|
195 | return rt *= d;
|
---|
196 | }
|
---|
197 |
|
---|
198 | template <int N, class T> inline
|
---|
199 | vec<N,T> operator * ( T d, const vec<N,T> & b )
|
---|
200 | { return b*d; }
|
---|
201 |
|
---|
202 | template <int N, class T> inline
|
---|
203 | vec<N,T> operator * ( const vec<N,T> & b, const vec<N,T> & d )
|
---|
204 | {
|
---|
205 | vec<N,T> rt(b);
|
---|
206 | return rt *= d;
|
---|
207 | }
|
---|
208 |
|
---|
209 | template <int N, class T> inline
|
---|
210 | vec<N,T> operator / ( const vec<N,T> & b, T d )
|
---|
211 | { vec<N,T> rt(b); return rt /= d; }
|
---|
212 |
|
---|
213 | template <int N, class T> inline
|
---|
214 | vec<N,T> operator + ( const vec<N,T> & v1, const vec<N,T> & v2 )
|
---|
215 | { vec<N,T> rt(v1); return rt += v2; }
|
---|
216 |
|
---|
217 | template <int N, class T> inline
|
---|
218 | vec<N,T> operator - ( const vec<N,T> & v1, const vec<N,T> & v2 )
|
---|
219 | { vec<N,T> rt(v1); return rt -= v2; }
|
---|
220 |
|
---|
221 |
|
---|
222 | template <int N, class T> inline
|
---|
223 | bool operator == ( const vec<N,T> & v1, const vec<N,T> & v2 )
|
---|
224 | {
|
---|
225 | for(int i = 0; i < N; i++)
|
---|
226 | if(v1.v[i] != v2.v[i])
|
---|
227 | return false;
|
---|
228 | return true;
|
---|
229 | }
|
---|
230 |
|
---|
231 | template <int N, class T> inline
|
---|
232 | bool operator != ( const vec<N,T> & v1, const vec<N,T> & v2 )
|
---|
233 | { return !(v1 == v2); }
|
---|
234 |
|
---|
235 |
|
---|
236 | typedef vec<3,unsigned char> vec3ub;
|
---|
237 | typedef vec<4,unsigned char> vec4ub;
|
---|
238 |
|
---|
239 |
|
---|
240 |
|
---|
241 |
|
---|
242 |
|
---|
243 | namespace GLH_REAL_NAMESPACE
|
---|
244 | {
|
---|
245 | typedef GLH_REAL real;
|
---|
246 |
|
---|
247 | class line;
|
---|
248 | class plane;
|
---|
249 | class matrix4;
|
---|
250 | class quaternion;
|
---|
251 | typedef quaternion rotation;
|
---|
252 |
|
---|
253 | class vec2 : public vec<2,real>
|
---|
254 | {
|
---|
255 | public:
|
---|
256 | vec2(const real & t = real()) : vec<2,real>(t)
|
---|
257 | {}
|
---|
258 | vec2(const vec<2,real> & t) : vec<2,real>(t)
|
---|
259 | {}
|
---|
260 | vec2(const real * tp) : vec<2,real>(tp)
|
---|
261 | {}
|
---|
262 |
|
---|
263 | vec2(real x, real y )
|
---|
264 | { v[0] = x; v[1] = y; }
|
---|
265 |
|
---|
266 | void get_value(real & x, real & y) const
|
---|
267 | { x = v[0]; y = v[1]; }
|
---|
268 |
|
---|
269 | vec2 & set_value( const real & x, const real & y)
|
---|
270 | { v[0] = x; v[1] = y; return *this; }
|
---|
271 |
|
---|
272 | };
|
---|
273 |
|
---|
274 |
|
---|
275 | class vec3 : public vec<3,real>
|
---|
276 | {
|
---|
277 | public:
|
---|
278 | vec3(const real & t = real()) : vec<3,real>(t)
|
---|
279 | {}
|
---|
280 | vec3(const vec<3,real> & t) : vec<3,real>(t)
|
---|
281 | {}
|
---|
282 | vec3(const real * tp) : vec<3,real>(tp)
|
---|
283 | {}
|
---|
284 |
|
---|
285 | vec3(real x, real y, real z)
|
---|
286 | { v[0] = x; v[1] = y; v[2] = z; }
|
---|
287 |
|
---|
288 | void get_value(real & x, real & y, real & z) const
|
---|
289 | { x = v[0]; y = v[1]; z = v[2]; }
|
---|
290 |
|
---|
291 | vec3 cross( const vec3 &rhs ) const
|
---|
292 | {
|
---|
293 | vec3 rt;
|
---|
294 | rt.v[0] = v[1]*rhs.v[2]-v[2]*rhs.v[1];
|
---|
295 | rt.v[1] = v[2]*rhs.v[0]-v[0]*rhs.v[2];
|
---|
296 | rt.v[2] = v[0]*rhs.v[1]-v[1]*rhs.v[0];
|
---|
297 | return rt;
|
---|
298 | }
|
---|
299 |
|
---|
300 | vec3 & set_value( const real & x, const real & y, const real & z)
|
---|
301 | { v[0] = x; v[1] = y; v[2] = z; return *this; }
|
---|
302 |
|
---|
303 | };
|
---|
304 |
|
---|
305 |
|
---|
306 | class vec4 : public vec<4,real>
|
---|
307 | {
|
---|
308 | public:
|
---|
309 | vec4(const real & t = real()) : vec<4,real>(t)
|
---|
310 | {}
|
---|
311 | vec4(const vec<4,real> & t) : vec<4,real>(t)
|
---|
312 | {}
|
---|
313 |
|
---|
314 | vec4(const vec<3,real> & t, real fourth)
|
---|
315 |
|
---|
316 | { v[0] = t.v[0]; v[1] = t.v[1]; v[2] = t.v[2]; v[3] = fourth; }
|
---|
317 | vec4(const real * tp) : vec<4,real>(tp)
|
---|
318 | {}
|
---|
319 | vec4(real x, real y, real z, real w)
|
---|
320 | { v[0] = x; v[1] = y; v[2] = z; v[3] = w; }
|
---|
321 |
|
---|
322 | void get_value(real & x, real & y, real & z, real & w) const
|
---|
323 | { x = v[0]; y = v[1]; z = v[2]; w = v[3]; }
|
---|
324 |
|
---|
325 | vec4 & set_value( const real & x, const real & y, const real & z, const real & w)
|
---|
326 | { v[0] = x; v[1] = y; v[2] = z; v[3] = w; return *this; }
|
---|
327 | };
|
---|
328 |
|
---|
329 | inline
|
---|
330 | vec3 homogenize(const vec4 & v)
|
---|
331 | {
|
---|
332 | vec3 rt;
|
---|
333 | assert(v.v[3] != GLH_ZERO);
|
---|
334 | rt.v[0] = v.v[0]/v.v[3];
|
---|
335 | rt.v[1] = v.v[1]/v.v[3];
|
---|
336 | rt.v[2] = v.v[2]/v.v[3];
|
---|
337 | return rt;
|
---|
338 | }
|
---|
339 |
|
---|
340 |
|
---|
341 |
|
---|
342 | class line
|
---|
343 | {
|
---|
344 | public:
|
---|
345 |
|
---|
346 | line()
|
---|
347 | { set_value(vec3(0,0,0),vec3(0,0,1)); }
|
---|
348 |
|
---|
349 | line( const vec3 & p0, const vec3 &p1)
|
---|
350 | { set_value(p0,p1); }
|
---|
351 |
|
---|
352 | void set_value( const vec3 &p0, const vec3 &p1)
|
---|
353 | {
|
---|
354 | position = p0;
|
---|
355 | direction = p1-p0;
|
---|
356 | direction.normalize();
|
---|
357 | }
|
---|
358 |
|
---|
359 | bool get_closest_points(const line &line2,
|
---|
360 | vec3 &pointOnThis,
|
---|
361 | vec3 &pointOnThat)
|
---|
362 | {
|
---|
363 |
|
---|
364 | // quick check to see if parallel -- if so, quit.
|
---|
365 | if(fabs(direction.dot(line2.direction)) == 1.0)
|
---|
366 | return 0;
|
---|
367 | line l2 = line2;
|
---|
368 |
|
---|
369 | // Algorithm: Brian Jean
|
---|
370 | //
|
---|
371 | register real u;
|
---|
372 | register real v;
|
---|
373 | vec3 Vr = direction;
|
---|
374 | vec3 Vs = l2.direction;
|
---|
375 | register real Vr_Dot_Vs = Vr.dot(Vs);
|
---|
376 | register real detA = real(1.0 - (Vr_Dot_Vs * Vr_Dot_Vs));
|
---|
377 | vec3 C = l2.position - position;
|
---|
378 | register real C_Dot_Vr = C.dot(Vr);
|
---|
379 | register real C_Dot_Vs = C.dot(Vs);
|
---|
380 |
|
---|
381 | u = (C_Dot_Vr - Vr_Dot_Vs * C_Dot_Vs)/detA;
|
---|
382 | v = (C_Dot_Vr * Vr_Dot_Vs - C_Dot_Vs)/detA;
|
---|
383 |
|
---|
384 | pointOnThis = position;
|
---|
385 | pointOnThis += direction * u;
|
---|
386 | pointOnThat = l2.position;
|
---|
387 | pointOnThat += l2.direction * v;
|
---|
388 |
|
---|
389 | return 1;
|
---|
390 | }
|
---|
391 |
|
---|
392 | vec3 get_closest_point(const vec3 &point)
|
---|
393 | {
|
---|
394 | vec3 np = point - position;
|
---|
395 | vec3 rp = direction*direction.dot(np)+position;
|
---|
396 | return rp;
|
---|
397 | }
|
---|
398 |
|
---|
399 | const vec3 & get_position() const {return position;}
|
---|
400 |
|
---|
401 | const vec3 & get_direction() const {return direction;}
|
---|
402 |
|
---|
403 | //protected:
|
---|
404 | vec3 position;
|
---|
405 | vec3 direction;
|
---|
406 | };
|
---|
407 |
|
---|
408 |
|
---|
409 |
|
---|
410 |
|
---|
411 |
|
---|
412 |
|
---|
413 |
|
---|
414 |
|
---|
415 |
|
---|
416 |
|
---|
417 |
|
---|
418 |
|
---|
419 |
|
---|
420 |
|
---|
421 |
|
---|
422 |
|
---|
423 |
|
---|
424 |
|
---|
425 |
|
---|
426 |
|
---|
427 |
|
---|
428 |
|
---|
429 |
|
---|
430 |
|
---|
431 |
|
---|
432 |
|
---|
433 |
|
---|
434 |
|
---|
435 |
|
---|
436 | // matrix
|
---|
437 |
|
---|
438 |
|
---|
439 | class matrix4
|
---|
440 | {
|
---|
441 |
|
---|
442 | public:
|
---|
443 |
|
---|
444 | matrix4() { make_identity(); }
|
---|
445 |
|
---|
446 | matrix4( real r )
|
---|
447 | { set_value(r); }
|
---|
448 |
|
---|
449 | matrix4( real * m )
|
---|
450 | { set_value(m); }
|
---|
451 |
|
---|
452 | matrix4( real a00, real a01, real a02, real a03,
|
---|
453 | real a10, real a11, real a12, real a13,
|
---|
454 | real a20, real a21, real a22, real a23,
|
---|
455 | real a30, real a31, real a32, real a33 )
|
---|
456 | {
|
---|
457 | element(0,0) = a00;
|
---|
458 | element(0,1) = a01;
|
---|
459 | element(0,2) = a02;
|
---|
460 | element(0,3) = a03;
|
---|
461 |
|
---|
462 | element(1,0) = a10;
|
---|
463 | element(1,1) = a11;
|
---|
464 | element(1,2) = a12;
|
---|
465 | element(1,3) = a13;
|
---|
466 |
|
---|
467 | element(2,0) = a20;
|
---|
468 | element(2,1) = a21;
|
---|
469 | element(2,2) = a22;
|
---|
470 | element(2,3) = a23;
|
---|
471 |
|
---|
472 | element(3,0) = a30;
|
---|
473 | element(3,1) = a31;
|
---|
474 | element(3,2) = a32;
|
---|
475 | element(3,3) = a33;
|
---|
476 | }
|
---|
477 |
|
---|
478 |
|
---|
479 | void get_value( real * mp ) const
|
---|
480 | {
|
---|
481 | int c = 0;
|
---|
482 | for(int j=0; j < 4; j++)
|
---|
483 | for(int i=0; i < 4; i++)
|
---|
484 | mp[c++] = element(i,j);
|
---|
485 | }
|
---|
486 |
|
---|
487 |
|
---|
488 | const real * get_value() const
|
---|
489 | { return m; }
|
---|
490 |
|
---|
491 | void set_value( real * mp)
|
---|
492 | {
|
---|
493 | int c = 0;
|
---|
494 | for(int j=0; j < 4; j++)
|
---|
495 | for(int i=0; i < 4; i++)
|
---|
496 | element(i,j) = mp[c++];
|
---|
497 | }
|
---|
498 |
|
---|
499 | void set_value( real r )
|
---|
500 | {
|
---|
501 | for(int i=0; i < 4; i++)
|
---|
502 | for(int j=0; j < 4; j++)
|
---|
503 | element(i,j) = r;
|
---|
504 | }
|
---|
505 |
|
---|
506 | void make_identity()
|
---|
507 | {
|
---|
508 | element(0,0) = 1.0;
|
---|
509 | element(0,1) = 0.0;
|
---|
510 | element(0,2) = 0.0;
|
---|
511 | element(0,3) = 0.0;
|
---|
512 |
|
---|
513 | element(1,0) = 0.0;
|
---|
514 | element(1,1) = 1.0;
|
---|
515 | element(1,2) = 0.0;
|
---|
516 | element(1,3) = 0.0;
|
---|
517 |
|
---|
518 | element(2,0) = 0.0;
|
---|
519 | element(2,1) = 0.0;
|
---|
520 | element(2,2) = 1.0;
|
---|
521 | element(2,3) = 0.0;
|
---|
522 |
|
---|
523 | element(3,0) = 0.0;
|
---|
524 | element(3,1) = 0.0;
|
---|
525 | element(3,2) = 0.0;
|
---|
526 | element(3,3) = 1.0;
|
---|
527 | }
|
---|
528 |
|
---|
529 |
|
---|
530 | static matrix4 identity()
|
---|
531 | {
|
---|
532 | static matrix4 mident (
|
---|
533 | 1.0, 0.0, 0.0, 0.0,
|
---|
534 | 0.0, 1.0, 0.0, 0.0,
|
---|
535 | 0.0, 0.0, 1.0, 0.0,
|
---|
536 | 0.0, 0.0, 0.0, 1.0 );
|
---|
537 | return mident;
|
---|
538 | }
|
---|
539 |
|
---|
540 |
|
---|
541 | void set_scale( real s )
|
---|
542 | {
|
---|
543 | element(0,0) = s;
|
---|
544 | element(1,1) = s;
|
---|
545 | element(2,2) = s;
|
---|
546 | }
|
---|
547 |
|
---|
548 | void set_scale( const vec3 & s )
|
---|
549 | {
|
---|
550 | element(0,0) = s.v[0];
|
---|
551 | element(1,1) = s.v[1];
|
---|
552 | element(2,2) = s.v[2];
|
---|
553 | }
|
---|
554 |
|
---|
555 |
|
---|
556 | void set_translate( const vec3 & t )
|
---|
557 | {
|
---|
558 | element(0,3) = t.v[0];
|
---|
559 | element(1,3) = t.v[1];
|
---|
560 | element(2,3) = t.v[2];
|
---|
561 | }
|
---|
562 |
|
---|
563 | void set_row(int r, const vec4 & t)
|
---|
564 | {
|
---|
565 | element(r,0) = t.v[0];
|
---|
566 | element(r,1) = t.v[1];
|
---|
567 | element(r,2) = t.v[2];
|
---|
568 | element(r,3) = t.v[3];
|
---|
569 | }
|
---|
570 |
|
---|
571 | void set_column(int c, const vec4 & t)
|
---|
572 | {
|
---|
573 | element(0,c) = t.v[0];
|
---|
574 | element(1,c) = t.v[1];
|
---|
575 | element(2,c) = t.v[2];
|
---|
576 | element(3,c) = t.v[3];
|
---|
577 | }
|
---|
578 |
|
---|
579 |
|
---|
580 | void get_row(int r, vec4 & t) const
|
---|
581 | {
|
---|
582 | t.v[0] = element(r,0);
|
---|
583 | t.v[1] = element(r,1);
|
---|
584 | t.v[2] = element(r,2);
|
---|
585 | t.v[3] = element(r,3);
|
---|
586 | }
|
---|
587 |
|
---|
588 | vec4 get_row(int r) const
|
---|
589 | {
|
---|
590 | vec4 v; get_row(r, v);
|
---|
591 | return v;
|
---|
592 | }
|
---|
593 |
|
---|
594 | void get_column(int c, vec4 & t) const
|
---|
595 | {
|
---|
596 | t.v[0] = element(0,c);
|
---|
597 | t.v[1] = element(1,c);
|
---|
598 | t.v[2] = element(2,c);
|
---|
599 | t.v[3] = element(3,c);
|
---|
600 | }
|
---|
601 |
|
---|
602 | vec4 get_column(int c) const
|
---|
603 | {
|
---|
604 | vec4 v; get_column(c, v);
|
---|
605 | return v;
|
---|
606 | }
|
---|
607 |
|
---|
608 | matrix4 inverse() const
|
---|
609 | {
|
---|
610 | matrix4 minv;
|
---|
611 |
|
---|
612 | real r1[8], r2[8], r3[8], r4[8];
|
---|
613 | real *s[4], *tmprow;
|
---|
614 |
|
---|
615 | s[0] = &r1[0];
|
---|
616 | s[1] = &r2[0];
|
---|
617 | s[2] = &r3[0];
|
---|
618 | s[3] = &r4[0];
|
---|
619 |
|
---|
620 | register int i,j,p,jj;
|
---|
621 | for(i=0;i<4;i++)
|
---|
622 | {
|
---|
623 | for(j=0;j<4;j++)
|
---|
624 | {
|
---|
625 | s[i][j] = element(i,j);
|
---|
626 | if(i==j) s[i][j+4] = 1.0;
|
---|
627 | else s[i][j+4] = 0.0;
|
---|
628 | }
|
---|
629 | }
|
---|
630 | real scp[4];
|
---|
631 | for(i=0;i<4;i++)
|
---|
632 | {
|
---|
633 | scp[i] = real(fabs(s[i][0]));
|
---|
634 | for(j=1;j<4;j++)
|
---|
635 | if(real(fabs(s[i][j])) > scp[i]) scp[i] = real(fabs(s[i][j]));
|
---|
636 | if(scp[i] == 0.0) return minv; // singular matrix!
|
---|
637 | }
|
---|
638 |
|
---|
639 | int pivot_to;
|
---|
640 | real scp_max;
|
---|
641 | for(i=0;i<4;i++)
|
---|
642 | {
|
---|
643 | // select pivot row
|
---|
644 | pivot_to = i;
|
---|
645 | scp_max = real(fabs(s[i][i]/scp[i]));
|
---|
646 | // find out which row should be on top
|
---|
647 | for(p=i+1;p<4;p++)
|
---|
648 | if(real(fabs(s[p][i]/scp[p])) > scp_max)
|
---|
649 | { scp_max = real(fabs(s[p][i]/scp[p])); pivot_to = p; }
|
---|
650 | // Pivot if necessary
|
---|
651 | if(pivot_to != i)
|
---|
652 | {
|
---|
653 | tmprow = s[i];
|
---|
654 | s[i] = s[pivot_to];
|
---|
655 | s[pivot_to] = tmprow;
|
---|
656 | real tmpscp;
|
---|
657 | tmpscp = scp[i];
|
---|
658 | scp[i] = scp[pivot_to];
|
---|
659 | scp[pivot_to] = tmpscp;
|
---|
660 | }
|
---|
661 |
|
---|
662 | real mji;
|
---|
663 | // perform gaussian elimination
|
---|
664 | for(j=i+1;j<4;j++)
|
---|
665 | {
|
---|
666 | mji = s[j][i]/s[i][i];
|
---|
667 | s[j][i] = 0.0;
|
---|
668 | for(jj=i+1;jj<8;jj++)
|
---|
669 | s[j][jj] -= mji*s[i][jj];
|
---|
670 | }
|
---|
671 | }
|
---|
672 | if(s[3][3] == 0.0) return minv; // singular matrix!
|
---|
673 |
|
---|
674 | //
|
---|
675 | // Now we have an upper triangular matrix.
|
---|
676 | //
|
---|
677 | // x x x x | y y y y
|
---|
678 | // 0 x x x | y y y y
|
---|
679 | // 0 0 x x | y y y y
|
---|
680 | // 0 0 0 x | y y y y
|
---|
681 | //
|
---|
682 | // we'll back substitute to get the inverse
|
---|
683 | //
|
---|
684 | // 1 0 0 0 | z z z z
|
---|
685 | // 0 1 0 0 | z z z z
|
---|
686 | // 0 0 1 0 | z z z z
|
---|
687 | // 0 0 0 1 | z z z z
|
---|
688 | //
|
---|
689 |
|
---|
690 | real mij;
|
---|
691 | for(i=3;i>0;i--)
|
---|
692 | {
|
---|
693 | for(j=i-1;j > -1; j--)
|
---|
694 | {
|
---|
695 | mij = s[j][i]/s[i][i];
|
---|
696 | for(jj=j+1;jj<8;jj++)
|
---|
697 | s[j][jj] -= mij*s[i][jj];
|
---|
698 | }
|
---|
699 | }
|
---|
700 |
|
---|
701 | for(i=0;i<4;i++)
|
---|
702 | for(j=0;j<4;j++)
|
---|
703 | minv(i,j) = s[i][j+4] / s[i][i];
|
---|
704 |
|
---|
705 | return minv;
|
---|
706 | }
|
---|
707 |
|
---|
708 |
|
---|
709 | matrix4 transpose() const
|
---|
710 | {
|
---|
711 | matrix4 mtrans;
|
---|
712 |
|
---|
713 | for(int i=0;i<4;i++)
|
---|
714 | for(int j=0;j<4;j++)
|
---|
715 | mtrans(i,j) = element(j,i);
|
---|
716 | return mtrans;
|
---|
717 | }
|
---|
718 |
|
---|
719 | matrix4 & mult_right( const matrix4 & b )
|
---|
720 | {
|
---|
721 | matrix4 mt(*this);
|
---|
722 | set_value(real(0));
|
---|
723 |
|
---|
724 | for(int i=0; i < 4; i++)
|
---|
725 | for(int j=0; j < 4; j++)
|
---|
726 | for(int c=0; c < 4; c++)
|
---|
727 | element(i,j) += mt(i,c) * b(c,j);
|
---|
728 | return *this;
|
---|
729 | }
|
---|
730 |
|
---|
731 | matrix4 & mult_left( const matrix4 & b )
|
---|
732 | {
|
---|
733 | matrix4 mt(*this);
|
---|
734 | set_value(real(0));
|
---|
735 |
|
---|
736 | for(int i=0; i < 4; i++)
|
---|
737 | for(int j=0; j < 4; j++)
|
---|
738 | for(int c=0; c < 4; c++)
|
---|
739 | element(i,j) += b(i,c) * mt(c,j);
|
---|
740 | return *this;
|
---|
741 | }
|
---|
742 |
|
---|
743 | // dst = M * src
|
---|
744 | void mult_matrix_vec( const vec3 &src, vec3 &dst ) const
|
---|
745 | {
|
---|
746 | real w = (
|
---|
747 | src.v[0] * element(3,0) +
|
---|
748 | src.v[1] * element(3,1) +
|
---|
749 | src.v[2] * element(3,2) +
|
---|
750 | element(3,3) );
|
---|
751 |
|
---|
752 | assert(w != GLH_ZERO);
|
---|
753 |
|
---|
754 | dst.v[0] = (
|
---|
755 | src.v[0] * element(0,0) +
|
---|
756 | src.v[1] * element(0,1) +
|
---|
757 | src.v[2] * element(0,2) +
|
---|
758 | element(0,3) ) / w;
|
---|
759 | dst.v[1] = (
|
---|
760 | src.v[0] * element(1,0) +
|
---|
761 | src.v[1] * element(1,1) +
|
---|
762 | src.v[2] * element(1,2) +
|
---|
763 | element(1,3) ) / w;
|
---|
764 | dst.v[2] = (
|
---|
765 | src.v[0] * element(2,0) +
|
---|
766 | src.v[1] * element(2,1) +
|
---|
767 | src.v[2] * element(2,2) +
|
---|
768 | element(2,3) ) / w;
|
---|
769 | }
|
---|
770 |
|
---|
771 | void mult_matrix_vec( vec3 & src_and_dst) const
|
---|
772 | { mult_matrix_vec(vec3(src_and_dst), src_and_dst); }
|
---|
773 |
|
---|
774 |
|
---|
775 | // dst = src * M
|
---|
776 | void mult_vec_matrix( const vec3 &src, vec3 &dst ) const
|
---|
777 | {
|
---|
778 | real w = (
|
---|
779 | src.v[0] * element(0,3) +
|
---|
780 | src.v[1] * element(1,3) +
|
---|
781 | src.v[2] * element(2,3) +
|
---|
782 | element(3,3) );
|
---|
783 |
|
---|
784 | assert(w != GLH_ZERO);
|
---|
785 |
|
---|
786 | dst.v[0] = (
|
---|
787 | src.v[0] * element(0,0) +
|
---|
788 | src.v[1] * element(1,0) +
|
---|
789 | src.v[2] * element(2,0) +
|
---|
790 | element(3,0) ) / w;
|
---|
791 | dst.v[1] = (
|
---|
792 | src.v[0] * element(0,1) +
|
---|
793 | src.v[1] * element(1,1) +
|
---|
794 | src.v[2] * element(2,1) +
|
---|
795 | element(3,1) ) / w;
|
---|
796 | dst.v[2] = (
|
---|
797 | src.v[0] * element(0,2) +
|
---|
798 | src.v[1] * element(1,2) +
|
---|
799 | src.v[2] * element(2,2) +
|
---|
800 | element(3,2) ) / w;
|
---|
801 | }
|
---|
802 |
|
---|
803 |
|
---|
804 | void mult_vec_matrix( vec3 & src_and_dst) const
|
---|
805 | { mult_vec_matrix(vec3(src_and_dst), src_and_dst); }
|
---|
806 |
|
---|
807 | // dst = M * src
|
---|
808 | void mult_matrix_vec( const vec4 &src, vec4 &dst ) const
|
---|
809 | {
|
---|
810 | dst.v[0] = (
|
---|
811 | src.v[0] * element(0,0) +
|
---|
812 | src.v[1] * element(0,1) +
|
---|
813 | src.v[2] * element(0,2) +
|
---|
814 | src.v[3] * element(0,3));
|
---|
815 | dst.v[1] = (
|
---|
816 | src.v[0] * element(1,0) +
|
---|
817 | src.v[1] * element(1,1) +
|
---|
818 | src.v[2] * element(1,2) +
|
---|
819 | src.v[3] * element(1,3));
|
---|
820 | dst.v[2] = (
|
---|
821 | src.v[0] * element(2,0) +
|
---|
822 | src.v[1] * element(2,1) +
|
---|
823 | src.v[2] * element(2,2) +
|
---|
824 | src.v[3] * element(2,3));
|
---|
825 | dst.v[3] = (
|
---|
826 | src.v[0] * element(3,0) +
|
---|
827 | src.v[1] * element(3,1) +
|
---|
828 | src.v[2] * element(3,2) +
|
---|
829 | src.v[3] * element(3,3));
|
---|
830 | }
|
---|
831 |
|
---|
832 | void mult_matrix_vec( vec4 & src_and_dst) const
|
---|
833 | { mult_matrix_vec(vec4(src_and_dst), src_and_dst); }
|
---|
834 |
|
---|
835 |
|
---|
836 | // dst = src * M
|
---|
837 | void mult_vec_matrix( const vec4 &src, vec4 &dst ) const
|
---|
838 | {
|
---|
839 | dst.v[0] = (
|
---|
840 | src.v[0] * element(0,0) +
|
---|
841 | src.v[1] * element(1,0) +
|
---|
842 | src.v[2] * element(2,0) +
|
---|
843 | src.v[3] * element(3,0));
|
---|
844 | dst.v[1] = (
|
---|
845 | src.v[0] * element(0,1) +
|
---|
846 | src.v[1] * element(1,1) +
|
---|
847 | src.v[2] * element(2,1) +
|
---|
848 | src.v[3] * element(3,1));
|
---|
849 | dst.v[2] = (
|
---|
850 | src.v[0] * element(0,2) +
|
---|
851 | src.v[1] * element(1,2) +
|
---|
852 | src.v[2] * element(2,2) +
|
---|
853 | src.v[3] * element(3,2));
|
---|
854 | dst.v[3] = (
|
---|
855 | src.v[0] * element(0,3) +
|
---|
856 | src.v[1] * element(1,3) +
|
---|
857 | src.v[2] * element(2,3) +
|
---|
858 | src.v[3] * element(3,3));
|
---|
859 | }
|
---|
860 |
|
---|
861 |
|
---|
862 | void mult_vec_matrix( vec4 & src_and_dst) const
|
---|
863 | { mult_vec_matrix(vec4(src_and_dst), src_and_dst); }
|
---|
864 |
|
---|
865 |
|
---|
866 | // dst = M * src
|
---|
867 | void mult_matrix_dir( const vec3 &src, vec3 &dst ) const
|
---|
868 | {
|
---|
869 | dst.v[0] = (
|
---|
870 | src.v[0] * element(0,0) +
|
---|
871 | src.v[1] * element(0,1) +
|
---|
872 | src.v[2] * element(0,2) ) ;
|
---|
873 | dst.v[1] = (
|
---|
874 | src.v[0] * element(1,0) +
|
---|
875 | src.v[1] * element(1,1) +
|
---|
876 | src.v[2] * element(1,2) ) ;
|
---|
877 | dst.v[2] = (
|
---|
878 | src.v[0] * element(2,0) +
|
---|
879 | src.v[1] * element(2,1) +
|
---|
880 | src.v[2] * element(2,2) ) ;
|
---|
881 | }
|
---|
882 |
|
---|
883 |
|
---|
884 | void mult_matrix_dir( vec3 & src_and_dst) const
|
---|
885 | { mult_matrix_dir(vec3(src_and_dst), src_and_dst); }
|
---|
886 |
|
---|
887 |
|
---|
888 | // dst = src * M
|
---|
889 | void mult_dir_matrix( const vec3 &src, vec3 &dst ) const
|
---|
890 | {
|
---|
891 | dst.v[0] = (
|
---|
892 | src.v[0] * element(0,0) +
|
---|
893 | src.v[1] * element(1,0) +
|
---|
894 | src.v[2] * element(2,0) ) ;
|
---|
895 | dst.v[1] = (
|
---|
896 | src.v[0] * element(0,1) +
|
---|
897 | src.v[1] * element(1,1) +
|
---|
898 | src.v[2] * element(2,1) ) ;
|
---|
899 | dst.v[2] = (
|
---|
900 | src.v[0] * element(0,2) +
|
---|
901 | src.v[1] * element(1,2) +
|
---|
902 | src.v[2] * element(2,2) ) ;
|
---|
903 | }
|
---|
904 |
|
---|
905 |
|
---|
906 | void mult_dir_matrix( vec3 & src_and_dst) const
|
---|
907 | { mult_dir_matrix(vec3(src_and_dst), src_and_dst); }
|
---|
908 |
|
---|
909 |
|
---|
910 | real & operator () (int row, int col)
|
---|
911 | { return element(row,col); }
|
---|
912 |
|
---|
913 | const real & operator () (int row, int col) const
|
---|
914 | { return element(row,col); }
|
---|
915 |
|
---|
916 | real & element (int row, int col)
|
---|
917 | { return m[row | (col<<2)]; }
|
---|
918 |
|
---|
919 | const real & element (int row, int col) const
|
---|
920 | { return m[row | (col<<2)]; }
|
---|
921 |
|
---|
922 | matrix4 & operator *= ( const matrix4 & mat )
|
---|
923 | {
|
---|
924 | mult_right( mat );
|
---|
925 | return *this;
|
---|
926 | }
|
---|
927 |
|
---|
928 | matrix4 & operator *= ( const real & r )
|
---|
929 | {
|
---|
930 | for (int i = 0; i < 4; ++i)
|
---|
931 | {
|
---|
932 | element(0,i) *= r;
|
---|
933 | element(1,i) *= r;
|
---|
934 | element(2,i) *= r;
|
---|
935 | element(3,i) *= r;
|
---|
936 | }
|
---|
937 | return *this;
|
---|
938 | }
|
---|
939 |
|
---|
940 | matrix4 & operator += ( const matrix4 & mat )
|
---|
941 | {
|
---|
942 | for (int i = 0; i < 4; ++i)
|
---|
943 | {
|
---|
944 | element(0,i) += mat.element(0,i);
|
---|
945 | element(1,i) += mat.element(1,i);
|
---|
946 | element(2,i) += mat.element(2,i);
|
---|
947 | element(3,i) += mat.element(3,i);
|
---|
948 | }
|
---|
949 | return *this;
|
---|
950 | }
|
---|
951 |
|
---|
952 | friend matrix4 operator * ( const matrix4 & m1, const matrix4 & m2 );
|
---|
953 | friend bool operator == ( const matrix4 & m1, const matrix4 & m2 );
|
---|
954 | friend bool operator != ( const matrix4 & m1, const matrix4 & m2 );
|
---|
955 |
|
---|
956 | //protected:
|
---|
957 | real m[16];
|
---|
958 | };
|
---|
959 |
|
---|
960 | inline
|
---|
961 | matrix4 operator * ( const matrix4 & m1, const matrix4 & m2 )
|
---|
962 | {
|
---|
963 | matrix4 product;
|
---|
964 |
|
---|
965 | product = m1;
|
---|
966 | product.mult_right(m2);
|
---|
967 |
|
---|
968 | return product;
|
---|
969 | }
|
---|
970 |
|
---|
971 | inline
|
---|
972 | bool operator ==( const matrix4 &m1, const matrix4 &m2 )
|
---|
973 | {
|
---|
974 | return (
|
---|
975 | m1(0,0) == m2(0,0) &&
|
---|
976 | m1(0,1) == m2(0,1) &&
|
---|
977 | m1(0,2) == m2(0,2) &&
|
---|
978 | m1(0,3) == m2(0,3) &&
|
---|
979 | m1(1,0) == m2(1,0) &&
|
---|
980 | m1(1,1) == m2(1,1) &&
|
---|
981 | m1(1,2) == m2(1,2) &&
|
---|
982 | m1(1,3) == m2(1,3) &&
|
---|
983 | m1(2,0) == m2(2,0) &&
|
---|
984 | m1(2,1) == m2(2,1) &&
|
---|
985 | m1(2,2) == m2(2,2) &&
|
---|
986 | m1(2,3) == m2(2,3) &&
|
---|
987 | m1(3,0) == m2(3,0) &&
|
---|
988 | m1(3,1) == m2(3,1) &&
|
---|
989 | m1(3,2) == m2(3,2) &&
|
---|
990 | m1(3,3) == m2(3,3) );
|
---|
991 | }
|
---|
992 |
|
---|
993 | inline
|
---|
994 | bool operator != ( const matrix4 & m1, const matrix4 & m2 )
|
---|
995 | { return !( m1 == m2 ); }
|
---|
996 |
|
---|
997 |
|
---|
998 |
|
---|
999 |
|
---|
1000 |
|
---|
1001 |
|
---|
1002 |
|
---|
1003 |
|
---|
1004 |
|
---|
1005 |
|
---|
1006 |
|
---|
1007 |
|
---|
1008 |
|
---|
1009 | class quaternion
|
---|
1010 | {
|
---|
1011 | public:
|
---|
1012 |
|
---|
1013 | quaternion()
|
---|
1014 | {
|
---|
1015 | *this = identity();
|
---|
1016 | }
|
---|
1017 |
|
---|
1018 | quaternion( const real v[4] )
|
---|
1019 | {
|
---|
1020 | set_value( v );
|
---|
1021 | }
|
---|
1022 |
|
---|
1023 |
|
---|
1024 | quaternion( real q0, real q1, real q2, real q3 )
|
---|
1025 | {
|
---|
1026 | set_value( q0, q1, q2, q3 );
|
---|
1027 | }
|
---|
1028 |
|
---|
1029 |
|
---|
1030 | quaternion( const matrix4 & m )
|
---|
1031 | {
|
---|
1032 | set_value( m );
|
---|
1033 | }
|
---|
1034 |
|
---|
1035 |
|
---|
1036 | quaternion( const vec3 &axis, real radians )
|
---|
1037 | {
|
---|
1038 | set_value( axis, radians );
|
---|
1039 | }
|
---|
1040 |
|
---|
1041 |
|
---|
1042 | quaternion( const vec3 &rotateFrom, const vec3 &rotateTo )
|
---|
1043 | {
|
---|
1044 | set_value( rotateFrom, rotateTo );
|
---|
1045 | }
|
---|
1046 |
|
---|
1047 | quaternion( const vec3 & from_look, const vec3 & from_up,
|
---|
1048 | const vec3 & to_look, const vec3& to_up)
|
---|
1049 | {
|
---|
1050 | set_value(from_look, from_up, to_look, to_up);
|
---|
1051 | }
|
---|
1052 |
|
---|
1053 | const real * get_value() const
|
---|
1054 | {
|
---|
1055 | return &q[0];
|
---|
1056 | }
|
---|
1057 |
|
---|
1058 | void get_value( real &q0, real &q1, real &q2, real &q3 ) const
|
---|
1059 | {
|
---|
1060 | q0 = q[0];
|
---|
1061 | q1 = q[1];
|
---|
1062 | q2 = q[2];
|
---|
1063 | q3 = q[3];
|
---|
1064 | }
|
---|
1065 |
|
---|
1066 | quaternion & set_value( real q0, real q1, real q2, real q3 )
|
---|
1067 | {
|
---|
1068 | q[0] = q0;
|
---|
1069 | q[1] = q1;
|
---|
1070 | q[2] = q2;
|
---|
1071 | q[3] = q3;
|
---|
1072 | counter = 0;
|
---|
1073 | return *this;
|
---|
1074 | }
|
---|
1075 |
|
---|
1076 | void get_value( vec3 &axis, real &radians ) const
|
---|
1077 | {
|
---|
1078 | radians = real(acos( q[3] ) * GLH_TWO);
|
---|
1079 | if ( radians == GLH_ZERO )
|
---|
1080 | axis = vec3( 0.0, 0.0, 1.0 );
|
---|
1081 | else
|
---|
1082 | {
|
---|
1083 | axis.v[0] = q[0];
|
---|
1084 | axis.v[1] = q[1];
|
---|
1085 | axis.v[2] = q[2];
|
---|
1086 | axis.normalize();
|
---|
1087 | }
|
---|
1088 | }
|
---|
1089 |
|
---|
1090 | void get_value( matrix4 & m ) const
|
---|
1091 | {
|
---|
1092 | real s, xs, ys, zs, wx, wy, wz, xx, xy, xz, yy, yz, zz;
|
---|
1093 |
|
---|
1094 | real norm = q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3];
|
---|
1095 |
|
---|
1096 | s = (equivalent(norm,GLH_ZERO)) ? GLH_ZERO : ( GLH_TWO / norm );
|
---|
1097 |
|
---|
1098 | xs = q[0] * s;
|
---|
1099 | ys = q[1] * s;
|
---|
1100 | zs = q[2] * s;
|
---|
1101 |
|
---|
1102 | wx = q[3] * xs;
|
---|
1103 | wy = q[3] * ys;
|
---|
1104 | wz = q[3] * zs;
|
---|
1105 |
|
---|
1106 | xx = q[0] * xs;
|
---|
1107 | xy = q[0] * ys;
|
---|
1108 | xz = q[0] * zs;
|
---|
1109 |
|
---|
1110 | yy = q[1] * ys;
|
---|
1111 | yz = q[1] * zs;
|
---|
1112 | zz = q[2] * zs;
|
---|
1113 |
|
---|
1114 | m(0,0) = real( GLH_ONE - ( yy + zz ));
|
---|
1115 | m(1,0) = real ( xy + wz );
|
---|
1116 | m(2,0) = real ( xz - wy );
|
---|
1117 |
|
---|
1118 | m(0,1) = real ( xy - wz );
|
---|
1119 | m(1,1) = real ( GLH_ONE - ( xx + zz ));
|
---|
1120 | m(2,1) = real ( yz + wx );
|
---|
1121 |
|
---|
1122 | m(0,2) = real ( xz + wy );
|
---|
1123 | m(1,2) = real ( yz - wx );
|
---|
1124 | m(2,2) = real ( GLH_ONE - ( xx + yy ));
|
---|
1125 |
|
---|
1126 | m(3,0) = m(3,1) = m(3,2) = m(0,3) = m(1,3) = m(2,3) = GLH_ZERO;
|
---|
1127 | m(3,3) = GLH_ONE;
|
---|
1128 | }
|
---|
1129 |
|
---|
1130 | quaternion & set_value( const real * qp )
|
---|
1131 | {
|
---|
1132 | memcpy(q,qp,sizeof(real) * 4);
|
---|
1133 |
|
---|
1134 | counter = 0;
|
---|
1135 | return *this;
|
---|
1136 | }
|
---|
1137 |
|
---|
1138 | quaternion & set_value( const matrix4 & m )
|
---|
1139 | {
|
---|
1140 | real tr, s;
|
---|
1141 | int i, j, k;
|
---|
1142 | const int nxt[3] = { 1, 2, 0 };
|
---|
1143 |
|
---|
1144 | tr = m(0,0) + m(1,1) + m(2,2);
|
---|
1145 |
|
---|
1146 | if ( tr > GLH_ZERO )
|
---|
1147 | {
|
---|
1148 | s = real(sqrt( tr + m(3,3) ));
|
---|
1149 | q[3] = real ( s * 0.5 );
|
---|
1150 | s = real(0.5) / s;
|
---|
1151 |
|
---|
1152 | q[0] = real ( ( m(1,2) - m(2,1) ) * s );
|
---|
1153 | q[1] = real ( ( m(2,0) - m(0,2) ) * s );
|
---|
1154 | q[2] = real ( ( m(0,1) - m(1,0) ) * s );
|
---|
1155 | }
|
---|
1156 | else
|
---|
1157 | {
|
---|
1158 | i = 0;
|
---|
1159 | if ( m(1,1) > m(0,0) )
|
---|
1160 | i = 1;
|
---|
1161 |
|
---|
1162 | if ( m(2,2) > m(i,i) )
|
---|
1163 | i = 2;
|
---|
1164 |
|
---|
1165 | j = nxt[i];
|
---|
1166 | k = nxt[j];
|
---|
1167 |
|
---|
1168 | s = real(sqrt( ( m(i,j) - ( m(j,j) + m(k,k) )) + GLH_ONE ));
|
---|
1169 |
|
---|
1170 | q[i] = real ( s * 0.5 );
|
---|
1171 | s = real(0.5 / s);
|
---|
1172 |
|
---|
1173 | q[3] = real ( ( m(j,k) - m(k,j) ) * s );
|
---|
1174 | q[j] = real ( ( m(i,j) + m(j,i) ) * s );
|
---|
1175 | q[k] = real ( ( m(i,k) + m(k,i) ) * s );
|
---|
1176 | }
|
---|
1177 |
|
---|
1178 | counter = 0;
|
---|
1179 | return *this;
|
---|
1180 | }
|
---|
1181 |
|
---|
1182 | quaternion & set_value( const vec3 &axis, real theta )
|
---|
1183 | {
|
---|
1184 | real sqnorm = axis.square_norm();
|
---|
1185 |
|
---|
1186 | if (sqnorm <= GLH_EPSILON)
|
---|
1187 | {
|
---|
1188 | // axis too small.
|
---|
1189 | x = y = z = 0.0;
|
---|
1190 | w = 1.0;
|
---|
1191 | }
|
---|
1192 | else
|
---|
1193 | {
|
---|
1194 | theta *= real(0.5);
|
---|
1195 | real sin_theta = real(sin(theta));
|
---|
1196 |
|
---|
1197 | if (!equivalent(sqnorm,GLH_ONE))
|
---|
1198 | sin_theta /= real(sqrt(sqnorm));
|
---|
1199 | x = sin_theta * axis.v[0];
|
---|
1200 | y = sin_theta * axis.v[1];
|
---|
1201 | z = sin_theta * axis.v[2];
|
---|
1202 | w = real(cos(theta));
|
---|
1203 | }
|
---|
1204 | return *this;
|
---|
1205 | }
|
---|
1206 |
|
---|
1207 | quaternion & set_value( const vec3 & rotateFrom, const vec3 & rotateTo )
|
---|
1208 | {
|
---|
1209 | vec3 p1, p2;
|
---|
1210 | real alpha;
|
---|
1211 |
|
---|
1212 | p1 = rotateFrom;
|
---|
1213 | p1.normalize();
|
---|
1214 | p2 = rotateTo;
|
---|
1215 | p2.normalize();
|
---|
1216 |
|
---|
1217 | alpha = p1.dot(p2);
|
---|
1218 |
|
---|
1219 | if(equivalent(alpha,GLH_ONE))
|
---|
1220 | {
|
---|
1221 | *this = identity();
|
---|
1222 | return *this;
|
---|
1223 | }
|
---|
1224 |
|
---|
1225 | // ensures that the anti-parallel case leads to a positive dot
|
---|
1226 | if(equivalent(alpha,-GLH_ONE))
|
---|
1227 | {
|
---|
1228 | vec3 v;
|
---|
1229 |
|
---|
1230 | if(p1.v[0] != p1.v[1] || p1.v[0] != p1.v[2])
|
---|
1231 | v = vec3(p1.v[1], p1.v[2], p1.v[0]);
|
---|
1232 | else
|
---|
1233 | v = vec3(-p1.v[0], p1.v[1], p1.v[2]);
|
---|
1234 |
|
---|
1235 | v -= p1 * p1.dot(v);
|
---|
1236 | v.normalize();
|
---|
1237 |
|
---|
1238 | set_value(v, GLH_PI);
|
---|
1239 | return *this;
|
---|
1240 | }
|
---|
1241 |
|
---|
1242 | p1 = p1.cross(p2);
|
---|
1243 | p1.normalize();
|
---|
1244 | set_value(p1,real(acos(alpha)));
|
---|
1245 |
|
---|
1246 | counter = 0;
|
---|
1247 | return *this;
|
---|
1248 | }
|
---|
1249 |
|
---|
1250 | quaternion & set_value( const vec3 & from_look, const vec3 & from_up,
|
---|
1251 | const vec3 & to_look, const vec3 & to_up)
|
---|
1252 | {
|
---|
1253 | quaternion r_look = quaternion(from_look, to_look);
|
---|
1254 |
|
---|
1255 | vec3 rotated_from_up(from_up);
|
---|
1256 | r_look.mult_vec(rotated_from_up);
|
---|
1257 |
|
---|
1258 | quaternion r_twist = quaternion(rotated_from_up, to_up);
|
---|
1259 |
|
---|
1260 | *this = r_twist;
|
---|
1261 | *this *= r_look;
|
---|
1262 | return *this;
|
---|
1263 | }
|
---|
1264 |
|
---|
1265 | quaternion & operator *= ( const quaternion & qr )
|
---|
1266 | {
|
---|
1267 | quaternion ql(*this);
|
---|
1268 |
|
---|
1269 | w = ql.w * qr.w - ql.x * qr.x - ql.y * qr.y - ql.z * qr.z;
|
---|
1270 | x = ql.w * qr.x + ql.x * qr.w + ql.y * qr.z - ql.z * qr.y;
|
---|
1271 | y = ql.w * qr.y + ql.y * qr.w + ql.z * qr.x - ql.x * qr.z;
|
---|
1272 | z = ql.w * qr.z + ql.z * qr.w + ql.x * qr.y - ql.y * qr.x;
|
---|
1273 |
|
---|
1274 | counter += qr.counter;
|
---|
1275 | counter++;
|
---|
1276 | counter_normalize();
|
---|
1277 | return *this;
|
---|
1278 | }
|
---|
1279 |
|
---|
1280 | void normalize()
|
---|
1281 | {
|
---|
1282 | real rnorm = GLH_ONE / real(sqrt(w * w + x * x + y * y + z * z));
|
---|
1283 | if (equivalent(rnorm, GLH_ZERO))
|
---|
1284 | return;
|
---|
1285 | x *= rnorm;
|
---|
1286 | y *= rnorm;
|
---|
1287 | z *= rnorm;
|
---|
1288 | w *= rnorm;
|
---|
1289 | counter = 0;
|
---|
1290 | }
|
---|
1291 |
|
---|
1292 | friend bool operator == ( const quaternion & q1, const quaternion & q2 );
|
---|
1293 |
|
---|
1294 | friend bool operator != ( const quaternion & q1, const quaternion & q2 );
|
---|
1295 |
|
---|
1296 | friend quaternion operator * ( const quaternion & q1, const quaternion & q2 );
|
---|
1297 |
|
---|
1298 | bool equals( const quaternion & r, real tolerance ) const
|
---|
1299 | {
|
---|
1300 | real t;
|
---|
1301 |
|
---|
1302 | t = (
|
---|
1303 | (q[0]-r.q[0])*(q[0]-r.q[0]) +
|
---|
1304 | (q[1]-r.q[1])*(q[1]-r.q[1]) +
|
---|
1305 | (q[2]-r.q[2])*(q[2]-r.q[2]) +
|
---|
1306 | (q[3]-r.q[3])*(q[3]-r.q[3]) );
|
---|
1307 | if(t > GLH_EPSILON)
|
---|
1308 | return false;
|
---|
1309 | return 1;
|
---|
1310 | }
|
---|
1311 |
|
---|
1312 | quaternion & conjugate()
|
---|
1313 | {
|
---|
1314 | q[0] *= -GLH_ONE;
|
---|
1315 | q[1] *= -GLH_ONE;
|
---|
1316 | q[2] *= -GLH_ONE;
|
---|
1317 | return *this;
|
---|
1318 | }
|
---|
1319 |
|
---|
1320 | quaternion & invert()
|
---|
1321 | {
|
---|
1322 | return conjugate();
|
---|
1323 | }
|
---|
1324 |
|
---|
1325 | quaternion inverse() const
|
---|
1326 | {
|
---|
1327 | quaternion r = *this;
|
---|
1328 | return r.invert();
|
---|
1329 | }
|
---|
1330 |
|
---|
1331 | //
|
---|
1332 | // Quaternion multiplication with cartesian vector
|
---|
1333 | // v' = q*v*q(star)
|
---|
1334 | //
|
---|
1335 | void mult_vec( const vec3 &src, vec3 &dst ) const
|
---|
1336 | {
|
---|
1337 | real v_coef = w * w - x * x - y * y - z * z;
|
---|
1338 | real u_coef = GLH_TWO * (src.v[0] * x + src.v[1] * y + src.v[2] * z);
|
---|
1339 | real c_coef = GLH_TWO * w;
|
---|
1340 |
|
---|
1341 | dst.v[0] = v_coef * src.v[0] + u_coef * x + c_coef * (y * src.v[2] - z * src.v[1]);
|
---|
1342 | dst.v[1] = v_coef * src.v[1] + u_coef * y + c_coef * (z * src.v[0] - x * src.v[2]);
|
---|
1343 | dst.v[2] = v_coef * src.v[2] + u_coef * z + c_coef * (x * src.v[1] - y * src.v[0]);
|
---|
1344 | }
|
---|
1345 |
|
---|
1346 | void mult_vec( vec3 & src_and_dst) const
|
---|
1347 | {
|
---|
1348 | mult_vec(vec3(src_and_dst), src_and_dst);
|
---|
1349 | }
|
---|
1350 |
|
---|
1351 | void scale_angle( real scaleFactor )
|
---|
1352 | {
|
---|
1353 | vec3 axis;
|
---|
1354 | real radians;
|
---|
1355 |
|
---|
1356 | get_value(axis, radians);
|
---|
1357 | radians *= scaleFactor;
|
---|
1358 | set_value(axis, radians);
|
---|
1359 | }
|
---|
1360 |
|
---|
1361 | static quaternion slerp( const quaternion & p, const quaternion & q, real alpha )
|
---|
1362 | {
|
---|
1363 | quaternion r;
|
---|
1364 |
|
---|
1365 | real cos_omega = p.x * q.x + p.y * q.y + p.z * q.z + p.w * q.w;
|
---|
1366 | // if B is on opposite hemisphere from A, use -B instead
|
---|
1367 |
|
---|
1368 | int bflip;
|
---|
1369 | if ( ( bflip = (cos_omega < GLH_ZERO)) )
|
---|
1370 | cos_omega = -cos_omega;
|
---|
1371 |
|
---|
1372 | // complementary interpolation parameter
|
---|
1373 | real beta = GLH_ONE - alpha;
|
---|
1374 |
|
---|
1375 | if(cos_omega >= GLH_ONE - GLH_EPSILON)
|
---|
1376 | return p;
|
---|
1377 |
|
---|
1378 | real omega = real(acos(cos_omega));
|
---|
1379 | real one_over_sin_omega = GLH_ONE / real(sin(omega));
|
---|
1380 |
|
---|
1381 | beta = real(sin(omega*beta) * one_over_sin_omega);
|
---|
1382 | alpha = real(sin(omega*alpha) * one_over_sin_omega);
|
---|
1383 |
|
---|
1384 | if (bflip)
|
---|
1385 | alpha = -alpha;
|
---|
1386 |
|
---|
1387 | r.x = beta * p.q[0]+ alpha * q.q[0];
|
---|
1388 | r.y = beta * p.q[1]+ alpha * q.q[1];
|
---|
1389 | r.z = beta * p.q[2]+ alpha * q.q[2];
|
---|
1390 | r.w = beta * p.q[3]+ alpha * q.q[3];
|
---|
1391 | return r;
|
---|
1392 | }
|
---|
1393 |
|
---|
1394 | static quaternion identity()
|
---|
1395 | {
|
---|
1396 | static quaternion ident( vec3( 0.0, 0.0, 0.0 ), GLH_ONE );
|
---|
1397 | return ident;
|
---|
1398 | }
|
---|
1399 |
|
---|
1400 | real & operator []( int i )
|
---|
1401 | {
|
---|
1402 | assert(i < 4);
|
---|
1403 | return q[i];
|
---|
1404 | }
|
---|
1405 |
|
---|
1406 | const real & operator []( int i ) const
|
---|
1407 | {
|
---|
1408 | assert(i < 4);
|
---|
1409 | return q[i];
|
---|
1410 | }
|
---|
1411 |
|
---|
1412 | protected:
|
---|
1413 |
|
---|
1414 | void counter_normalize()
|
---|
1415 | {
|
---|
1416 | if (counter > GLH_QUATERNION_NORMALIZATION_THRESHOLD)
|
---|
1417 | normalize();
|
---|
1418 | }
|
---|
1419 |
|
---|
1420 | union
|
---|
1421 | {
|
---|
1422 | struct
|
---|
1423 | {
|
---|
1424 | real q[4];
|
---|
1425 | };
|
---|
1426 | struct
|
---|
1427 | {
|
---|
1428 | real x;
|
---|
1429 | real y;
|
---|
1430 | real z;
|
---|
1431 | real w;
|
---|
1432 | };
|
---|
1433 | };
|
---|
1434 |
|
---|
1435 | // renormalization counter
|
---|
1436 | unsigned char counter;
|
---|
1437 | };
|
---|
1438 |
|
---|
1439 | inline
|
---|
1440 | bool operator == ( const quaternion & q1, const quaternion & q2 )
|
---|
1441 | {
|
---|
1442 | return (equivalent(q1.x, q2.x) &&
|
---|
1443 | equivalent(q1.y, q2.y) &&
|
---|
1444 | equivalent(q1.z, q2.z) &&
|
---|
1445 | equivalent(q1.w, q2.w) );
|
---|
1446 | }
|
---|
1447 |
|
---|
1448 | inline
|
---|
1449 | bool operator != ( const quaternion & q1, const quaternion & q2 )
|
---|
1450 | {
|
---|
1451 | return ! ( q1 == q2 );
|
---|
1452 | }
|
---|
1453 |
|
---|
1454 | inline
|
---|
1455 | quaternion operator * ( const quaternion & q1, const quaternion & q2 )
|
---|
1456 | {
|
---|
1457 | quaternion r(q1);
|
---|
1458 | r *= q2;
|
---|
1459 | return r;
|
---|
1460 | }
|
---|
1461 |
|
---|
1462 |
|
---|
1463 |
|
---|
1464 |
|
---|
1465 |
|
---|
1466 |
|
---|
1467 |
|
---|
1468 |
|
---|
1469 |
|
---|
1470 |
|
---|
1471 | class plane
|
---|
1472 | {
|
---|
1473 | public:
|
---|
1474 |
|
---|
1475 | plane()
|
---|
1476 | {
|
---|
1477 | planedistance = 0.0;
|
---|
1478 | planenormal.set_value( 0.0, 0.0, 1.0 );
|
---|
1479 | }
|
---|
1480 |
|
---|
1481 |
|
---|
1482 | plane( const vec3 &p0, const vec3 &p1, const vec3 &p2 )
|
---|
1483 | {
|
---|
1484 | vec3 v0 = p1 - p0;
|
---|
1485 | vec3 v1 = p2 - p0;
|
---|
1486 | planenormal = v0.cross(v1);
|
---|
1487 | planenormal.normalize();
|
---|
1488 | planedistance = p0.dot(planenormal);
|
---|
1489 | }
|
---|
1490 |
|
---|
1491 | plane( const vec3 &normal, real distance )
|
---|
1492 | {
|
---|
1493 | planedistance = distance;
|
---|
1494 | planenormal = normal;
|
---|
1495 | planenormal.normalize();
|
---|
1496 | }
|
---|
1497 |
|
---|
1498 | plane( const vec3 &normal, const vec3 &point )
|
---|
1499 | {
|
---|
1500 | planenormal = normal;
|
---|
1501 | planenormal.normalize();
|
---|
1502 | planedistance = point.dot(planenormal);
|
---|
1503 | }
|
---|
1504 |
|
---|
1505 | void offset( real d )
|
---|
1506 | {
|
---|
1507 | planedistance += d;
|
---|
1508 | }
|
---|
1509 |
|
---|
1510 | bool intersect( const line &l, vec3 &intersection ) const
|
---|
1511 | {
|
---|
1512 | vec3 pos, dir;
|
---|
1513 | vec3 pn = planenormal;
|
---|
1514 | real pd = planedistance;
|
---|
1515 |
|
---|
1516 | pos = l.get_position();
|
---|
1517 | dir = l.get_direction();
|
---|
1518 |
|
---|
1519 | if(dir.dot(pn) == 0.0) return 0;
|
---|
1520 | pos -= pn*pd;
|
---|
1521 | // now we're talking about a plane passing through the origin
|
---|
1522 | if(pos.dot(pn) < 0.0) pn.negate();
|
---|
1523 | if(dir.dot(pn) > 0.0) dir.negate();
|
---|
1524 | vec3 ppos = pn * pos.dot(pn);
|
---|
1525 | pos = (ppos.length()/dir.dot(-pn))*dir;
|
---|
1526 | intersection = l.get_position();
|
---|
1527 | intersection += pos;
|
---|
1528 | return 1;
|
---|
1529 | }
|
---|
1530 | void transform( const matrix4 &matrix )
|
---|
1531 | {
|
---|
1532 | matrix4 invtr = matrix.inverse();
|
---|
1533 | invtr = invtr.transpose();
|
---|
1534 |
|
---|
1535 | vec3 pntOnplane = planenormal * planedistance;
|
---|
1536 | vec3 newPntOnplane;
|
---|
1537 | vec3 newnormal;
|
---|
1538 |
|
---|
1539 | invtr.mult_dir_matrix(planenormal, newnormal);
|
---|
1540 | matrix.mult_vec_matrix(pntOnplane, newPntOnplane);
|
---|
1541 |
|
---|
1542 | newnormal.normalize();
|
---|
1543 | planenormal = newnormal;
|
---|
1544 | planedistance = newPntOnplane.dot(planenormal);
|
---|
1545 | }
|
---|
1546 |
|
---|
1547 | bool is_in_half_space( const vec3 &point ) const
|
---|
1548 | {
|
---|
1549 |
|
---|
1550 | if(( point.dot(planenormal) - planedistance) < 0.0)
|
---|
1551 | return 0;
|
---|
1552 | return 1;
|
---|
1553 | }
|
---|
1554 |
|
---|
1555 |
|
---|
1556 | real distance( const vec3 & point ) const
|
---|
1557 | {
|
---|
1558 | return planenormal.dot(point - planenormal*planedistance);
|
---|
1559 | }
|
---|
1560 |
|
---|
1561 | const vec3 &get_normal() const
|
---|
1562 | {
|
---|
1563 | return planenormal;
|
---|
1564 | }
|
---|
1565 |
|
---|
1566 |
|
---|
1567 | real get_distance_from_origin() const
|
---|
1568 | {
|
---|
1569 | return planedistance;
|
---|
1570 | }
|
---|
1571 |
|
---|
1572 |
|
---|
1573 | friend bool operator == ( const plane & p1, const plane & p2 );
|
---|
1574 |
|
---|
1575 |
|
---|
1576 | friend bool operator != ( const plane & p1, const plane & p2 );
|
---|
1577 |
|
---|
1578 | //protected:
|
---|
1579 | vec3 planenormal;
|
---|
1580 | real planedistance;
|
---|
1581 | };
|
---|
1582 |
|
---|
1583 | inline
|
---|
1584 | bool operator == (const plane & p1, const plane & p2 )
|
---|
1585 | {
|
---|
1586 | return ( p1.planedistance == p2.planedistance && p1.planenormal == p2.planenormal);
|
---|
1587 | }
|
---|
1588 |
|
---|
1589 | inline
|
---|
1590 | bool operator != ( const plane & p1, const plane & p2 )
|
---|
1591 | { return ! (p1 == p2); }
|
---|
1592 |
|
---|
1593 |
|
---|
1594 |
|
---|
1595 | } // "ns_##GLH_REAL"
|
---|
1596 |
|
---|
1597 | // make common typedefs...
|
---|
1598 | #ifdef GLH_REAL_IS_FLOAT
|
---|
1599 | typedef GLH_REAL_NAMESPACE::vec2 vec2f;
|
---|
1600 | typedef GLH_REAL_NAMESPACE::vec3 vec3f;
|
---|
1601 | typedef GLH_REAL_NAMESPACE::vec4 vec4f;
|
---|
1602 | typedef GLH_REAL_NAMESPACE::quaternion quaternionf;
|
---|
1603 | typedef GLH_REAL_NAMESPACE::quaternion rotationf;
|
---|
1604 | typedef GLH_REAL_NAMESPACE::line linef;
|
---|
1605 | typedef GLH_REAL_NAMESPACE::plane planef;
|
---|
1606 | typedef GLH_REAL_NAMESPACE::matrix4 matrix4f;
|
---|
1607 | #endif
|
---|
1608 |
|
---|
1609 |
|
---|
1610 |
|
---|
1611 |
|
---|
1612 | } // namespace glh
|
---|
1613 |
|
---|
1614 |
|
---|
1615 |
|
---|
1616 | #endif
|
---|
1617 |
|
---|